This invention relates to digital filtering of sampled signals and in an important example to filtering of digital video
The sampling rate of a digital video has to be changed for converting between different formats. For example, in order to save bandwidth a video signal may be stored and transmitted in a low resolution format but displayed in an up converted high resolution format. Typically, the sampling rate of the low resolution is related to the sampling rate of the high resolution by a ratio 1:M or by a ratio N:M where N and M are integers. Depending on the application, several cascades of up and down conversion filtering can occur. For example in a broadcast chain this is due to repeated editing, preview and storage operations. In order to achieve a perfect reconstruction of those parts of the pictures that have not been changed by editing operations up conversion from the low resolution to the high resolution and subsequent down conversion should result in a transparent cascade. Transparent cascading of N:M up and M:N down conversion filtering imposes additional problems on the filter design when compared with a cascade of up and down conversion filters for ratios 1:M and M:1.
It is an object of one aspect of the present invention to provide an improved digital filtering process capable of transparent up conversion and cascaded down conversion.
Accordingly, the present invention consists in one aspect in a digital filtering process for achieving a transparent cascade on N:M up conversion and subsequent M:N down conversion, where the up and down conversion ratios N:M and M:N respectively are rational numbers and the integers N and M satisfy the condition 1 less than N less than M, wherein the up conversion filter operates on a sampled signal Sinput and is chosen to take the form sup(n)=xcexa3sinput(k).g(Nnxe2x88x92Mk) and wherein a corresponding down conversion filter operates on the up converted signal sup and is chosen to take the form sdown(n)=xcexa3sup(k).h(Mnxe2x88x92Nk); the pair (g,h) of up and down conversion filters being chosen so that xcexa3h(Mnxe2x88x92Nk).g(Nkxe2x88x92Mm) is equal to unity if n=m and, is otherwise equal to zero.